TY - JOUR ID - 13167 TI - Toeplitz and Hankel Operators on a Vector-valued Bergman Space JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Das, Namita AD - Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, 751004,, Odisha, India Y1 - 2015 PY - 2015 VL - 1 IS - 2 SP - 230 EP - 242 KW - Bergman space KW - Toeplitz operators KW - little Hankel operators KW - strong-operator topology KW - finite rank operators DO - 10.22034/kjm.2015.13167 N2 - In this paper, we derive certain algebraic properties of Toeplitz and Hankel operators defined on the vector-valued Bergman spaces $L_a^{2, \mathbb{C}^n}(\mathbb{D})$, where $\mathbb{D}$ is the open unit disk in $\mathbb{C}$ and $n\geq 1.$ We show that the set of all Toeplitz operators $T_{\Phi}, \Phi\in L_{M_n}^{\infty}(\mathbb{D})$ is strongly dense in the set of all bounded linear operators ${\mathcal L}(L_a^{2, \mathbb{C}^n}(\mathbb{D}))$ and characterize all finite rank little Hankel operators. UR - https://www.kjm-math.org/article_13167.html L1 - https://www.kjm-math.org/article_13167_cd3e86baa83715a9bf967ed60c149d34.pdf ER -